“In 100 years of bare-knuckle fighting in the United States, which terminated around 1897 with a John L Sullivan heavyweight championship fight, there wasn’t a single ring fatality. Today, there are three or four every year in the US, and around 15 per cent of professional fighters suffer some form of permanent brain damage during their career.”

I don't like the explanation that there are fewer deaths therefore bareknuckle is safer; there are so many reasons this can be true; I'm guessing this has something to do with it:

I would think there would be a greater chance of concusion with bare knuckle though.

On what basis do you think this? A concussion is a deep-tissue injury. Deep-tissue injuries are easier to inflict when your own surface areas are protected (as in American football). Why would boxing-versus-bareknuckle show any difference in this regard?